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On butterfly-points in β X , Tychonoff products and weak Lindelöf numbers

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

Let X be the Tychonoff product α < τ X α of τ -many Tychonoff non-single point spaces X α . Let p X * be a point in the closure of some G X whose weak Lindelöf number is strictly less than the cofinality of τ . Then we show that β X { p } is not normal. Under some additional assumptions, p is a butterfly-point in β X . In particular, this is true if either X = ω τ or X = R τ and τ is infinite and not countably cofinal.

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